We first calculate the optical depth of the dust in the accretion flow.
Given
the large uncertainties on the dust opacity (see Section REF ), we take a crude approach and let the dust opacity
be independent of density and temperature in the region where dust is present (\(T<{T_{\textnormal {dest}}}\) , or \(r>{R_{\textnormal {dest}}}\) )A test with the weak powerlaw dependence \(\kappa \propto T^{1/2}\)  appropriate for the “metal grains”
regime of [1]} indeed did not lead to a significantly different optical depth..
The contribution of the dust to the optical depth through the accreting matter is given by
\(\tau _{\mathrm {dust,\,H}\,\alpha }= \int _{R_{\textnormal {dest}}}^{r_{\rm max}}f_{\textrm {d/g}}\kappa _{\bullet ,\,\mathrm {H}\,\alpha }\,\rho \,dr,\) 
